A Derived Matter-Relaxation Channel in Late-Time Cosmology

Persistent discrepancies between early- and late-universe cosmological inferences, especially the Hubble-constant tension and the late-time clustering tension usually summarized by S8, motivate minimal extensions of the standard flat ΛCDM framework. Earlier versions of this manuscript tested a one-parameter effective matter-dissolution model motivated by the Fractal Consistency Law (FCL), in which the standard continuity equation for pressureless matter is deformed by a dimensionless attenuation parameter Γ. This version upgrades the theoretical status of that parameter. Instead of treating Γ only as a fitted phenomenological coefficient, we introduce a conditional derivation from a structural-relief principle: matter is interpreted as a stabilized defect class of a fractal substrate, and the effective matter attenuation arises because the mass cost of such defects relaxes as the large-scale texture of the universe approaches an admissible consistency attractor. The central result is the Theorem of Structural Relief. If particle number is conserved while the effective structural mass cost varies as m(a) = m0 Ω(a), then the modified continuity equation ρ̇m + 3Hρm = −Γ(a)Hρm corresponds not to literal particle disappearance, but to mass-cost relaxation, with Γ(a) = −d ln Ω / d ln a. In the constant-relaxation limit this gives m(a) = m0 a−Γ. A further FCL closure is proposed by tying the asymptotic value of Γ to an admissibility gap measured relative to a large-scale consistency attractor, Γ∞ = ΔA / φ0, with φ0 = ln(6π5). For ΔA = 0.1201, this yields Γ∞ ≃ 0.01598. This value is presented as a derived prediction of a new restricted submodel, not as completed empirical validation until the corresponding full likelihood, CMB, DESI-mock, and raw-chain analyses are rerun. The paper then formulates a late-activation function Γ(a) = Γ∞ S(a), designed to preserve the early-time success of ΛCDM while allowing a structurally motivated relaxation channel to become active only after the emergence of the large-scale attractor regime. The staged inference architecture is retained: late-time probes only (S1), late-time probes plus CMB-lite anchoring (S2), and stronger Planck-informed anchoring (S3). Existing constant-Γ results are reported as the current empirical baseline, while the derived-Γ module is identified as the decisive next falsifiable step.